That's a common pattern of aggression transference: when somebody offends you, you get angry and are very likely to transfer your aggression onto other people, in most cases onto those absolutely extraneous to the conflict you were involved in.
My idea is suppresion aggression transference through realization of its simple mechanism. When feeling angry offended by somebody, always keep in mind the true cause of your anger and frustration. Also try not to keep this tension inside - when suppressed this way it may be harmful to you health; try to direct it to some non-destructive practical or symbolical activities, by drawing some complex shapes with a pencil or by making origami characters from paper. Another suppression method is speaking out about the causes of your anger to your friend, pet or teddy-bear.
Just never allow it splash out at innocent people.